The diameter of the circle is the segment AB and it is known that A (0; -6) and B (0; 2) form the equation of the circle.

In this part of the task, the diameter AB of the circle is given, where A (0; -6) and B (0; 2). It is required to draw up the equation of the circle. Obviously, the center of the circle (which we denote by C (x0; y0)) is in the middle of the segment AB. We have: x0 = (0 + 0) / 2 = 0 and y0 = (-6 + 2) / 2 = -2. We calculate the length of the diameter AB = √ ((0 – 0) ² + (2 – (-6)) ²) = 8. Then the radius of the circle is 8: 2 = 4. Therefore, the desired equation has the form: x² + (y + 2 ) ² = 16.